I am dealing with the following problem for some time now:
Suppose you have these two functions: $T_x^{-1}:\:x\:=\:x'\:+\:t_3\cdot \sin\left(\frac{2\cdot \:\pi \:\cdot \:y'}{t_1}\right)$ and $T_y^{-1}:\:y\:=\:y'\:+\:t_4\cdot \:\sin\left(\frac{2\cdot \:\:\pi \:\:\cdot \:\:x'}{t_2}\right)$, where $t_1$, $t_2$, $t_3$ and $t_4$ are given constants. From these two functions I want to find $T_x$ and $T_y$, so it means that I want $x'$ to depend only on $x$ and $y$, and I want $y'$ to depend only on $x$ and $y$.
Can someone help me with this problem?